Thanks for contacting us. Technical climbing over 6000meters is never going to NOT leave you huffing and puffing unless you are very well acclimated. Could it be that your issue is more related to lack of acclimatization than it is to fitness?
Your question 1)
If you are confident that you are well acclimated to 6000+ meters and still having this problem then it is worth considering ways to improve fitness even further. Less than vertical routes require the legs to do most of the work in propelling you upward. Your legs have 2-4 times more muscle mass than your arms, they also typically contain a much higher percentage of slow twitch muscle. This means they use a lot more oxygen than the arms will AND are more easily endurance trained.
The real issue with true quadrupedal movement like climbing steeper terrain is that; ever since our predecessors stood up, our hearts have evolved for bipedal locomotion. They are relatively smaller than quadrupedal mammals. We are starting off with an built in design limitation.
Your question 2)
See above but your legs are the limiter here not your arms unless you are climbing overhanging routes at 7000m.
Your question 3)
At 6000m you cannot get anywhere near the power level or HR of Anaerobic Threshold or maxVO2 for more than a few seconds. There is just not enough oxygen to support that power output. This is why the basic aerobic capacity, as measured by the Aerobic Threshold, is such a good predictor of high altitude performance. Read this article for more explanation: https://www.uphillathlete.com/goettlersteckkhumbutraining/.
There will be some gains in endurance from training at around and above AnT and that may contribute a small amount to your overall performance. BUT it is the basic aerobic capacity at AeT which is the engine that is getting you up those big climbs. Maximal oxygen uptake, as measured by maxVO2, has a very poor correlation with high altitude climbing performance so don’t waste time and mental energy worrying about that nearly untrainable (at your age) quantity.
Work on increasing your power at the Aerobic Threshold if you want to climb big mountains faster.